Journal of Combinatorics

Volume 3 (2012)

Number 3

Rees products and lexicographic shellability

Pages: 243 – 276

DOI: http://dx.doi.org/10.4310/JOC.2012.v3.n3.a1

Authors

Svante Linusson (Department of Mathematics, KTH-Royal Institute of Technology, Stockholm, Sweden)

John Shareshian (Department of Mathematics, Washington University, St. Louis, Missouri, U.S.A.)

Michelle L. Wachs (Department of Mathematics, University of Miami, Coral Gables, Florida, U.S.A.)

Abstract

We use the theory of lexicographic shellability to provide various examples in which the rank of the homology of a Rees product of two partially ordered sets enumerates some set of combinatorial objects, perhaps according to some natural statistic on the set. Many of these examples generalize a result of J. Jonsson, which says that the rank of the unique nontrivial homology group of the Rees product of a truncated Boolean algebra of degree $n$ and a chain of length $n-1$ is the number of derangements in ${\mathfrak S}_n$.

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